Problem 90 - A Complete Resource Book in Chemistry for JEE Main

Question

How much chlorine will be liberated on passing one ampere current for 30 min through \(\mathrm{NaCl}\) solution? (a) \(0.66 \mathrm{~mol}\) (b) \(0.33 \mathrm{~mol}\) (c) \(0.66 \mathrm{~g}\) (d) \(0.33 \mathrm{~g}\)

Step-by-Step Solution

Answer

Chlorine liberated is approximately 0.66 g, option (c).

Step 1: Determine the Total Charge Passed

First, calculate the total charge (Q) that has passed through the sodium chloride (NaCl) solution. We can use the formula \( Q = I \times t \), where \( I = 1 \text{ A} \) (ampere) is the current, and \( t = 30 \times 60 = 1800 \text{ s} \) (seconds) is the time. Therefore, \( Q = 1 \times 1800 = 1800 \text{ C} \) (coulombs).

Step 2: Use Faraday's Law to Find Moles of Electrons

Faraday's law states that the amount of substance liberated at an electrode is directly proportional to the number of moles of electrons (n) used, given by \( n = \frac{Q}{F} \), where \( F = 96485 \text{ C/mol} \) (Faraday's constant). Substituting the values, we get \( n = \frac{1800}{96485} \approx 0.01865 \text{ moles of electrons}.\)

Step 3: Determine Moles of Chlorine Liberated

In the electrolysis of \( \mathrm{NaCl} \), chlorine gas \( \mathrm{Cl_2} \) is liberated at the anode. Each \( \mathrm{Cl_2} \) molecule requires 2 electrons to be formed. Therefore, the moles of chlorine gas produced is \( \frac{0.01865}{2} \approx 0.009325 \text{ moles of } \mathrm{Cl_2}.\)

Step 4: Convert Moles to Grams

The molar mass of chlorine gas \( \mathrm{Cl_2} \) is \( 2 \times 35.5 = 71 \text{ g/mol}.\) By multiplying the moles of chlorine by its molar mass, we find the mass: \( 0.009325 \times 71 \approx 0.662 \text{ g}.\)

Step 5: Select the Correct Answer From Options

Based on our calculations, approximately \( 0.66 \text{ g} \) of chlorine is liberated. So, the correct answer is (c) \( 0.66 \text{ g}.\)

Key Concepts

Faraday's Law

Faraday's Law is a fundamental concept in electrochemistry that helps us understand how electrical energy contributes to chemical reactions. It is named after Michael Faraday, and it states that the amount of substance deposited or dissolved during electrolysis is proportional to the amount of electrical charge transferred.
In mathematical terms, if you want to find out the moles of electrons responsible for a reaction, use the formula:

• \( n = \frac{Q}{F} \)
• where \( n \) is the number of moles of electrons, \( Q \) is the total charge in coulombs, and \( F \) is Faraday's constant (\( 96485 \text{ C/mol} \)).

This relationship is incredibly useful in electrolysis as it links the charged particles (electrons) with the substances being produced or consumed in the cell. Faraday's Law essentially tells us how many moles of electrons are needed for a reaction, enabling precise calculations.

Chlorine Liberation

Chlorine liberation is the process of releasing chlorine gas during the electrolysis of sodium chloride (\( \mathrm{NaCl} \)) in an aqueous solution. When an electrical current passes through the solution, the ions in the salt separate and move towards their respective electrodes.
For chlorine liberation:

• Anions (\( \mathrm{Cl^-} \)) migrate to the anode (positive electrode) where they lose electrons. This process is called oxidation.
• Oxidation of chloride ions forms chlorine gas (\( \mathrm{Cl_2} \)).

In this process, each molecule of chlorine (\( \mathrm{Cl_2} \)) requires two chloride ions, meaning two electrons are needed to release one molecule of chlorine gas. This reaction is pivotal in many industrial processes where chlorine gas is used.

Electrochemical Calculation

Electrochemical calculations are central to understanding and predicting the outcomes of reactions in electrochemistry. These calculations involve converting measurements of electric current and time into chemical quantities like moles of substances.
In the provided exercise, we calculated how much chlorine is liberated by:

• Firstly determining the total electric charge (\( Q \)): \( Q = I \times t \), where \( I \) is the current and \( t \) is the time in seconds.
• Using Faraday's Law, \( Q \) was converted into moles of electrons, \( n = \frac{Q}{F} \).
• Finally, the moles of electrons help in finding the moles of chlorine gas produced.

Each step ensures precision and provides a means to effectively calculate real quantities from electrical data.

Current and Charge

In electrochemistry, current and charge are crucial since they determine how much of a chemical compound is formed or decomposed during electrolysis. **Current** refers to the continuous flow of electric charge, measured in amperes (A). **Charge**, on the other hand, is the total electric power transferred over time, and is measured in coulombs (C).
The relationship between these is given by:

• \( Q = I \times t \)
• where \( Q \) is charge (C), \( I \) is current (A), and \( t \) is time (seconds).

These concepts are fundamental for tasks such as determining how much substance has reacted in electrolysis. Understanding how current and charge interrelate means that students can accurately determine the outcome of the electrochemical reactions taking place in their experiments.